Insolvency Forecasting through Trend Analysis with Full Ignorance of Probabilities

17 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 INSOLVENCY FORECASTING THROUGH TREND ANALYSIS WITHFULL IGNORANCE OFPROBABILITIES1 Tomáš Poláček, Ma ké a K un o ádo á* Abs ac The complex iews o  insol ency p oceedings a e unique, poo ly known, in e disciplina y and mul idimensional, e en hough he e is a b oad spec um o  di e en BM (Bank up cy Models). The e o e, i iso en p ohibi i ely di icul omake o ecas s using nume ical quan i ie s and adi ional s a is ical me hods. Theleas in o ma ion-in ensi e end alues a eused: posi i e, inc easing, ze o, cons an , nega i e, dec easing. Thesolu ion o a end model isase o scena ios whe e X is hese o  a iables quan i ied by he ends. All possible ansi ions among hescena ios a egene a ed. Ano ien ed ansi ional g aph has ase o scena ios asnodes and he ansi ions asa cs. Ano ien ed pa h desc ibes any possible u u e andpas ime beha iou o  hebank up cy sys em unde s udy. The g aph ep esen s he comple e lis o  o ecas s based on ends. Aneigh -dimensional model se es asacase s udy. On he ansi ional g aph o  hecase s udy model, decision ee heu is ics a eused o calcula ing hep obabili ies o  he e minal scena ios andpossible payo s. Keywo ds: o ecas , insol ency, end, quali a i e, bank up cy, ansi ion JEL Classi ica ion: G33, G34 In oduc ion A his ime, along wi h he inc easing numbe o insol ency p oceedings, e o s a e being made o s eamline p ocesses and iden i y links be ween majo i y c edi o s (M ázo á and Z i inský, 2015). These a e concu en wi h da a mining in es iga ions o ind di e en ways o e ec i ely sol ing insol ency p oceedings in a ious egions o he Czech Republic (M ázo á and Z i inský, 2014). Mo e and mo e p o essional esea ch is conce ned wi h he ques ion o why he numbe o insol ency p oceedings o bo h legal and na u al pe sons is inc easing (Paseko á and C ho á Kude o á, 2014). Some s udies a e ocused on he desc ip i e s a e o he domes ic ma ke o e a ce ain pe iod a e he in oduc ion o he Insol ency Ac (Sm čka, Schőn eld and Še čík, 2013) o wha e ec he amendmen s and amendmen s o he ac i sel ha e on he p ac ice, which add essed some o he undamen al issues ega ding powe s in decision-making in insol ency p oceedings (Rich e , 2013). Few scien i ic s udies deal wi h he eco e y o claims om insol ency p oceedings, o na u al o legal pe sons, o o p ac ical solu ions o insol ency ha a ec a ious ma ke de e minan s (Jakubík, 2007). 1 This pape was suppo ed by g an s FP-S-18-5074 “De elopmen ends o he economic managemen o he en e p ise in he Eu opean economic en i onmen ”. * B no Uni e si y o Technology, Facul y o Business and Managemen (polacek@ bm. u b .cz; k un o ado a@ bm. u b .cz). 18 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 Insol ency p oceedings as such a e subjec o he in luence o many ac o s om he whole economic en i onmen . Some ac o s (de e minan s) canno be quan i ied and basic s a is ical models canno be used (Sen, Singe , 1994). So, he use o end esea ch is app op ia e (Vícha and Dohnal, 2008; Dohnal, 2016). This means ha knowledge i ems o di e en le els o subjec i i y mus be aken in o conside a ion o de elop he bes possible model o a unique ask unde s udy. The e o e, many bank up cy obse a ions a e equi ed. Howe e , hey a e no a ailable. This is he eason why in o ma ion non-in ensi e o mal ools a e used mo e and mo e equen ly, see e.g. uzzy and/o ough se s (Pa láko á Dočekalo á and Kocmano á, 2016; Meluzín e al., 2016). 1. Al e na i e Decision-Making Me hods in heP ocess Decision-making analyses a e o en used o help decision-make s choose be ween al e na i es based on he expec ed u ili y associa ed wi h he unc ion o i s consequences and po en ial impac s. The e o e, o example, in a s udy (Wang e al., 2018) a mul ic i e ia decision model is de eloped. Al hough many success ul s udies ha e been conduc ed on he de ec ion o bank up cy, a ely ha e p obabilis ic app oaches been made. In esea ch (An unes, Ribei o and Pe ei a, 2017), a p obabilis ic aspec is assumed by applying Gaussian p ocesses. Bank up cy and eo ganisa ion p edic ion models a e o en used in audi ing la ge co po a e ansac ions (me ge s and acquisi ions, s a egic alliances, e c.), in making in es men decisions and in he judicia y, whe e judges a e inal a bi a o s in bank up cy p oceedings. Howe e , all exis ing insol ency models a e inadequa e mainly because he esea ch me hods we e de ec i e. The au ho s me ely pu igid ma hema ical models in o bank up cy. Models do no ollow an in e disciplina y app oach, do no allow op imisa ion and simula ion o de i e he bes condi ions o minimising inancial h ea s. The s udy (Nwogugu, 2006) p esen s a ious dynamic models o insol ency decision-making and de elops he amewo k and basis o u he esea ch in o he use o dynamic sys ems and a i icial in elligence in modelling bank up cy decisions and legal a gumen s. This pape deals wi h bank up cy o ecas ing unde condi ions o se e e in o ma ion sho ages. Such bank up cies a e o en desc ibed by non-nume ical quan i ie s, e.g. wo ds – low, medium, high. Howe e , he ans e o such e bal alues in o uzzy se s is e y subjec i e (Yi-Chung Hu and Tseng, 2007). 2. T end Models The e a e many di e en in e p e a ions o end concep s (Kams and Kennedy, 1998; S ekle and Syming on, 2016). The end concep s as i is used in his pape is based on ou alues (Vicha and Dohnal, 2008; B edeweg, 2009): Posi i e Ze o Nega i e Any Value (1) + 0 - * An equa ionless end model M is a se o w pai -wise ela ions M = Ps (Xi, Xj) (2) s = 1, 2, ……w 19 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 Examples/shapes o he ela ions P (2) a e gi en in Figu e 1: Figu e 1 | T ends ela ionships Y X Y X Y X Y X Y X Y X 25 25 25 26 22 23 33 33 3 26 24 22 21 21 23 25 22 24 26 X Y Y Y Y Y Y X X X X X Sou ce: Au ho s` own p ocessing An algo i hm, which can be used o sol e he model (2), is based on he p uning o a specially gene a ed ee o combina ions. I is no he goal o his pape o desc ibe such an algo i hm, as i is a pu ely ma hema ical combina o ial ask (Vicha and Dohnal, 2008). The model (2) is sol ed and he se o n dimensional scena ios is ob ained S(n, m). The e a e m scena ios: S(n, m) = (X1, DX1, DDX1), (X2, DX2, DDX2),…, (Xn, DXn, DDXn)j, (3) j = 1, 2,…, m, whe e DX is he i s and DDX is he second ime end de i a i es. Fo example, he ollowing h ee-dimensional scena io, n = 3 (3). X1 X2 X3 (4) (+ + +) (+ - 0) (+ - -). The model (2) is sol ed and he se o n dimensional scena ios is ob ained S(n, m). The e a e m scena ios: 20 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 2.1 T ansi ional G aphs The se o scena ios S (3) is no he only esul o a end modelling. I is possible o gene a e ansi ions among he se o scena ios. Figu e 2 | A end desc ip ion o aquan i a i e oscilla ion (+0-) (0+0) (+++) (+0+) (+--) (+-+) (0+0) (++-) Time Sou ce: Au ho s` own p ocessing The iple s gi en in Figu e 2 desc ibe a b oad spec um o di e en oscilla ions, e.g. dumped oscilla ion o i egula oscilla ions wi h andomly o de e minis ically changing equencies and/o ampli udes. 3. Case S udy Based on he heu is ics o using end me hods, a iables ha ha e a majo impac on he deb elie p ocess ha e been ca e ully selec ed a e discussions wi h insol ency expe s. In he nex chap e , he a iables will be desc ibed wi h an explana ion o how hei exis ence indi idually a ec s he insol ency p ocess. Subsequen ly, hese a iables we e used o build a end model based on ime-dependen insol ency managemen scena ios. The e a e no published end models o bank up cies. A eam o wo expe s was con ac ed and he lis o case s udy a iables was gene a ed: SEL Selling o Asse s ENJ Ensu ed Jus ice GRD Le el o G eed TAX Tax Bu den SAT Sa is ac ion o C edi o s (5) SOL Solu ion o Deb o s Asse s POL Poli ical In luence BUL Bullying o C edi o s INF In la ion 21 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 Selling o asse s In p inciple, i is igh ha a secu ed c edi o would decide on how he p ope y o he c edi o is secu ed. Howe e , he p ac ice is mo e complex and e lec s a numbe o pa ial in e es s o he subjec s who immedia ely decide on he me hod o mone isa ion and, in his sense, hey ins uc he insol ency adminis a o . Al hough he insol ency us ee may e use he o de s o he hedged c edi o i hey conside ha he objec o he hedge can be mone ised mo e ad an ageously. Ensu ed jus ice I is a a iable ha ep esen s he mo al and ai beha iou o he insol ency cou , which should pe o m a ca aly ic and independen ole in he insol ency p ocess. The insol ency cou is he egional cou whe e he deb o `s insol ency p oceedings a e conduc ed. I i is a legal en i y, i is a egional cou in he egion whe e he deb o is based. In he case o a na u al pe son, i is he cou whe e he deb o esides. Le el o g eed The le el o g eed is a a iable unde s ood in end modelling as he i a ional beha iou o he deb o , which pushes agains o he a iables o amo isa ion o he deb and he sa is ac ion o he c edi o `s equi emen s. I has been selec ed as an impo an ac o in he en i e insol ency p ocess and is also a sui able a iable o end modelling in e ms o i s agueness and di icul y in quan i ying. Tax bu den Fo end modelling pu poses, he ax load a iable is applied as a con adic o y cons an (depending on he ype o deb o /c edi o and he case o which he insol ency p oceedings a e dedica ed). Unlike o he p ocess a iables, i is o a sha p na u e. Sa is ac ion o c edi o s Sa is ac ion o c edi o s is he i s o he a iables ha a e pe cei ed in he model as a ge a iables o ep esen he bes possible s a e o he ques ion unde in es iga ion. I is a ai paymen o deb s o c edi o s om deb o s whe e, based on he cou `s decision, he c edi o (s) and c edi o commi ees a e spli in o secu ed and unsecu ed. Solu ion o deb o asse s In he end decision model, his a iable is seen as one o he goals ha should be as cos - e ec i e as possible o he subjec , so ha he c edi o `s claim and he economic and social s a us o he deb o a e main ained. Poli ical in luence I is no possible o analyse he coun y`s economy by only aking in o accoun ma ke ac o s (Radu, 2015). E e y economic sys em mus be in eg a ed and ha monized wi h he coun y`s con inuing de elopmen , a end ha e lec s echnological change and inno a ion as well as poli ical con lic s ha lead o he ep esen a ion and changing o di e en in e es s and ins i u ions. The e o e, i is impo an o include poli ical ac o s o analyse he economic p ocess (Boye , 2011) 22 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 Bullying o c edi o s Being bullied by a c edi o is agains he law. Al hough c edi o s ha e many op ions o claim hei igh o epaymen o he deb , which is conside ed legal, he e a e also many p ac ices ha a e widely used ha a e no law ul (Ki wan, 2018). The ini ia ion o insol ency p oceedings no only has nega i e legal consequences (e.g. limi ing he alleged deb o in ela ion o he handling o his p ope y) bu also has non-legal consequences (damage o he alleged deb o `s epu a ion, doub o his c edibili y and economic si ua ion). In la ion Simple in la ion e e s o an inc ease in he p ice le el. In e e yday li e, an inc ease in in la ion may mean ha consume s pay mo e a a g oce y s o e o , o example, a a pe ol s a ion (Vicki, 2017). Inc eased in la ion also a ec s se ices and hei p o ide s. These ade s need o adjus hei se ice p ices adequa ely o in la iona y de elopmen s because hei ising cos s a e dependen on inc easing supplie s` p ices and can ha e a di ec e ec on he en i e deb o /c edi o sys em. 2.1 Model o Insol ency P oceedings Build a iables (5), which play an impo an ole in he decision-making p ocess, and o m a comple e se o scena ios, we e selec ed a e discussions wi h expe s on insol ency. The e y na u e o he a iables used sugges s ha i is e y di icul o quan i y, see, o example, GRD. The e o e, he use o end models is jus i ied. See e.g. Figu e 1 T ends ela ionship 1, (1) X Y 1 + SEL ENJ 2 25 SEL GRD 3 21 SEL SAT 4 24 SEL SOL 5 23 ENJ TAX (6) 6 - ENJ BUL 7 + TAX POL 8 - SAT BUL 9 + POL INF 23 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 The e a e 23 scena ios, m = 23(6). # SEL ENJ GRD TAX SAT SOL POL BUL INF V V V V G G O O O 1 +++ +++ +-- +++ +++ +-+ +++ +-- +++ 2 +++ +++ +-- +++ +++ +-0 +++ +-- +++ 3 +++ +++ +-- +++ +++ +-- +++ +-- +++ 4 +++ +++ +-- ++0 +++ +-+ ++0 +-- ++0 5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0 6 +++ +++ +-- ++0 +++ +-- ++0 +-- ++0 7 +++ +++ +-- ++- +++ +-+ ++- +-- ++- 8 +++ +++ +-- ++- +++ +-0 ++- +-- ++- 9 +++ +++ +-- ++- +++ +-- ++- +-- ++- 10 ++- ++- +-+ ++- ++- +-+ ++- +-+ ++- 11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+ 12 +00 +00 +00 +00 +00 +00 +00 +00 +00 (7) 13 +0- +0- +0+ +0- +0- +0+ +0- +0+ +0- 14 +-+ +-+ ++- +-+ +-+ +++ +-+ ++- +-+ 15 +-+ +-+ ++- +-+ +-+ ++0 +-+ ++- +-+ 16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+ 17 +-+ +-+ ++- +-0 +-+ +++ +-0 ++- +-0 18 +-+ +-+ ++- +-0 +-+ ++0 +-0 ++- +-0 19 +-+ +-+ ++- +-0 +-+ ++- +-0 ++- +-0 20 +-+ +-+ ++- +-- +-+ +++ +-- ++- +-- 21 +-+ +-+ ++- +-- +-+ ++0 +-- ++- +-- 22 +-+ +-+ ++- +-- +-+ ++- +-- ++- +-- 23 +-- +-- +++ +-- +-- +++ +-- +++ +-- Figu e 3 | T ansi ion g aph based onase o 23 scena ios (7) 10 13 23 12 16 15 11 19 22 21 20 17 18 14 7 4 8 3 9 6 2 5 1 Sou ce: Au ho s` own p ocessing 24 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 Any o ecas ing is hea ily p ede e mined by in e p e a ions o a iables (5). The choice o he se s V, O, G, is o c ucial impo ance and is based on he cu en poin o iew. Any o ecas ing/decision-making will be based on an n-dimensional model M(X). A se X o n a iables is a union o Decision a iables V, Goals a iables G and O -con ol a iables O (8). SEL V Selling o Asse s ENJ V Ensu ed Jus ice GRD V Le el o G eed TAX O Tax SAT G Sa is ac ion o he C edi o s (8) SOL G Solu ion o Deb o `s Asse s POL O Poli ical In luence BUL V Bullying o C edi o s INF O In la ion O = [POL, INF, TAX] G = [SAT, SOL] (9) V = [SEL, ENJ, GRD, BUL] A simple common-sense analysis indica es ha he e is one iew and o ecas om he c edi o `s poin o iew: Figu e 4 | C edi o `s iew – whe e ep esen s a a iable ime SAT SOL Sou ce: Au ho s` own p ocessing The bes end desc ip ion o he c edi o `s iew: SAT Inc ease mo e and mo e apidly DSAT = + DDSAT = + SOL Dec easing mo e and mo e slowly DSOL = - DDSOL = + (10) The wo s end desc ip ion o he c edi o `s iew: SAT Dec easing mo e and mo e slowly DSAT = - DDSAT = + SOL Inc ease mo e and mo e apidly DSOL = + DDSOL = + (11) 25 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625 The bes scena io is S7 (7). The sho es pa h is he pa h leading om he wo s scena io S16 o he a ge scena io S7 (see Figu e 3): S16 →S11 →S3 →S5 →S7 (12) Figu e 5 | Asimpli ied ansi ion g aph based onase o 23 scena ios (7) 16 3 5 711 Sou ce: Au ho s` own p ocessing The sequence o scena ios is, see (23): No. SEL ENJ GRD TAX SAT SOL POL BUL INF V V V V G G O O O 16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+ 11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+ (13) 3 +++ +++ +-- +++ +++ +-- +++ +-- +++ 5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0 7 +++ +++ +-- ++- +++ +-+ ++- +-- ++- A decision-make has no ee choice o change he a iables (5). Some a iables a e no unde his/he con ol (8). The e o e, he e a e a iables selec ed by O as ou o con ol. This means ha any o ecas is pa ially based on a ailable desc ip ions o O a iables (13) e.g. p obabili y dis ibu ions. 3.2 P obabili y Dis ibu ions Based on he ansi ional g aph om he case s udy in Figu e 5, he pa h om he wo s kind o scena io o he bes kind o scena io acco ding o he c edi o ´s poin o iew was used. The ansi ion g aph in Figu e 3 has been ans o med in o a decision ee whe e some o he decision-making heu is ics can be used o ob aining he p obabili ies and o de e mina e he o ecas . The esul ing e minal scena ios, which also e lec he posi i e s a us o c edi o s, we e designa ed as e mina ion poin s. Whe e S16 was designa ed as he oo node and S7 was he e mina ion node (wi h he o he s S1, S8 and S9). Whe e he e mina ion scena ios ha e sligh ly di e en ou pu s. Figu e 6 | The ansi ion g aph has been ans o med in o adecision ee (7) 2 16 1 7 89 5 4 3 11 6 Sou ce: Au ho s` own p ocessing